Toric anti-self-dual Einstein metrics via complex geometry

Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the classification of general toric anti-self-dual metrics given in an earlier paper (math.DG/0602423). The results complement the work of Calderbank-Pedersen (math.DG/0105263), who describe where the Einstein metrics appear amongst the Joyce spaces, leading to a different classification. Taking the twistor transform of our result gives a new proof of their theorem.Comment: v2. Published version. Additional references. 14 page

Toric anti-self-dual 4-manifolds via complex geometry

Using the twistor correspondence, this article gives a one-to-one correspondence between germs of toric anti-self-dual conformal classes and certain holomorphic data determined by the induced action on twistor space. Recovering the metric from the holomorphic data leads to the classical problem of prescribing the Cech coboundary of 0-cochains on an elliptic curve covered by two annuli. The classes admitting Kahler representatives are described; each such class contains a circle of Kahler metrics. This gives new local examples of scalar-flat Kahler surfaces and generalises work of Joyce who considered the case where the distribution orthogonal to the torus action is integrable.Comment: 25 pages, 2 figures, v2 corrected some misprints, v3 corrected more misprints, published version (minus one typo

Off-shell N=2 tensor supermultiplets

A multiplet calculus is presented for an arbitrary number n of N=2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkahler or quaternion-Kahler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kahler manifolds with two commuting isometries is given.Comment: 36 page

A holonomy characterisation of Fefferman spaces

We prove that Fefferman spaces, associated to non--degenerate CR structures of hypersurface type, are characterised, up to local conformal isometry, by the existence of a parallel orthogonal complex structure on the standard tractor bundle. This condition can be equivalently expressed in terms of conformal holonomy. Extracting from this picture the essential consequences at the level of tensor bundles yields an improved, conformally invariant analogue of Sparling's characterisation of Fefferman spaces.Comment: AMSLaTeX, 15 page

On NS5-brane instantons and volume stabilization

We study general aspects of NS5-brane instantons in relation to the stabilization of the volume modulus in Calabi-Yau compactifications of type II strings with fluxes, and their orientifold versions. These instantons correct the Kahler potential and generically yield significant contributions to the scalar potential at intermediate values of string coupling constant and volume. Under suitable conditions they yield uplifting terms that allow for meta--stable de Sitter vacua.Comment: 29 pages, 3 figures; statements about fields G^a made more precise, added some clarifications, typos correcte

The twistor spinors of generic 2- and 3-distributions

Generic distributions on 5- and 6-manifolds give rise to conformal structures that were discovered by P. Nurowski resp. R. Bryant. We describe both as Fefferman-type constructions and show that for orientable distributions one obtains conformal spin structures. The resulting conformal spin geometries are then characterized by their conformal holonomy and equivalently by the existence of a twistor spinor which satisfies a genericity condition. Moreover, we show that given such a twistor spinor we can decompose a conformal Killing field of the structure. We obtain explicit formulas relating conformal Killing fields, almost Einstein structures and twistor spinors.Comment: 26 page

Domain walls of N=2 supergravity in five dimensions from hypermultiplet moduli spaces

We study domain wall solutions in d=5, N=2 supergravity coupled to a single hypermultiplet whose moduli space is described by certain inhomogeneous, toric ESD manifolds constructed recently by Calderbank and Singer. Upon gauging a generic U(1) isometry of these spaces, we obtain an infinite family of models whose "superpotential" admits an arbitrary number of isolated critical points. By investigating the associated supersymmetric flows, we prove the existence of domain walls of Randall-Sundrum type for each member of our family, and find chains of domain walls interpolating between various AdS_5 backgrounds. Our models are described by a discrete infinity of smooth and complete one-hypermultiplet moduli spaces, which live on an open subset of the minimal resolution of certain cyclic quotient singularities. These spaces generalize the Pedersen metrics considered recently by Behrndt and Dall' Agata.Comment: 39 pages, numerous figures; v4: two references adde

M-theory on `toric' G_2 cones and its type II reduction

We analyze a class of conical G_2 metrics admitting two commuting isometries, together with a certain one-parameter family of G_2 deformations which preserves these symmetries. Upon using recent results of Calderbank and Pedersen, we write down the explicit G_2 metric for the most general member of this family and extract the IIA reduction of M-theory on such backgrounds, as well as its type IIB dual. By studying the asymptotics of type II fields around the relevant loci, we confirm the interpretation of such backgrounds in terms of localized IIA 6-branes and delocalized IIB 5-branes. In particular, we find explicit, general expressions for the string coupling and R-R/NS-NS forms in the vicinity of these objects. Our solutions contain and generalize the field configurations relevant for certain models considered in recent work of Acharya and Witten.Comment: 45 pages, references adde

Intersecting 6-branes from new 7-manifolds with G_2 holonomy

We discuss a new family of metrics of 7-manifolds with G_2 holonomy, which are R^3 bundles over a quaternionic space. The metrics depend on five parameters and have two Abelian isometries. Certain singularities of the G_2 manifolds are related to fixed points of these isometries; there are two combinations of Killing vectors that possess co-dimension four fixed points which yield upon compactification only intersecting D6-branes if one also identifies two parameters. Two of the remaining parameters are quantized and we argue that they are related to the number of D6-branes, which appear in three stacks. We perform explicitly the reduction to the type IIA model.Comment: 25 pages, 1 figure, Latex, small changes and add refs, version appeared in JHE

K\"{a}hler-Einstein metrics on strictly pseudoconvex domains

The metrics of S. Y. Cheng and S.-T. Yau are considered on a strictly pseudoconvex domains in a complex manifold. Such a manifold carries a complete K\"{a}hler-Einstein metric if and only if its canonical bundle is positive. We consider the restricted case in which the CR structure on $\partial M$ is normal. In this case M must be a domain in a resolution of the Sasaki cone over $\partial M$. We give a condition on a normal CR manifold which it cannot satisfy if it is a CR infinity of a K\"{a}hler-Einstein manifold. We are able to mostly determine those normal CR 3-manifolds which can be CR infinities. Many examples are given of K\"{a}hler-Einstein strictly pseudoconvex manifolds on bundles and resolutions.Comment: 30 pages, 1 figure, couple corrections, improved a couple example